New Proof of the Fukui Conjecture by the Functional Asymptotic Linearity Theorem

The present article provides a new proof of the Fukui conjecture concerning the additivity problem of the zero-point vibrational energies of hydrocarbons. This conjecture played a prominent role in the initial development of the repeat space theory (RST), and continues to be of vital significance in the recent development of the theory of the generalized repeat space X _r (q,d). The new proof of the Fukui conjecture has been given here by establishing the functional version of the Asymptotic Linearity Theorem (ALT), the Functional ALT. This enhanced version of the ALT directly implies the validity of the Fukui conjecture; it easily unifies, in a broad perspective, a variety of additivity phenomena in physico-chemical network systems having many identical moieties, and efficiently solves some interpretational problems of the empirical additivity formulae from experimental chemistry. The proof of the functional version of the ALT is based on a new method transferable to the extended theoretical framework of the generalized repeat space X _r (q,d).     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Repeat space theory applied to carbon nanotubes and related molecular networks. III

The present article is part III of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. In this part III, four problems concerning the above-mentioned extension of the RST have been formulated. Affirmative solutions of these problems imply (i) asymptotic analysis of carbon nanotubes (CNTs) via the new techniques of normed repeat space, Banach algebra, and C*-algebra becomes possible; (ii) a new linkage is formed between the investigations of CNTs and those of ‘spectral symmetry’. In the present paper, we give affirmative solutions to all of the four problems, together with (a) estimates of the norms of matrix sequences representing CNTs, (b) Challenging Problem A^#, which complements Problems A, (c) several pictures of ‘CNT Matrix Art’ which has heuristic power to lead one to get the affirmative answers to the problems formulated in an abstract algebraic manner.     

A g-Type Lysozyme from Deep-Sea Hydrothermal Vent Shrimp Kills Selectively Gram-Negative Bacteria

Lysozyme is a key effector molecule of the innate immune system in both vertebrate and invertebrate. It is classified into six types, one of which is the goose-type (g-type). To date, no study on g-type lysozyme in crustacean has been documented. Here, we report the identification and characterization of a g-type lysozyme (named LysG1) from the shrimp inhabiting a deep-sea hydrothermal vent in Manus Basin. LysG1 possesses conserved structural features of g-type lysozymes. The recombinant LysG1 (rLysG1) exhibited no muramidase activity and killed selectively Gram-negative bacteria in a manner that depended on temperature, pH, and metal ions. rLysG1 bound target bacteria via interaction with bacterial cell wall components, notably lipopolysaccharide (LPS), and induced cellular membrane permeabilization, which eventually caused cell lysis. The endotoxin-binding capacity enabled rLysG1 to alleviate the inflammatory response induced by LPS. Mutation analysis showed that the bacterial binding and killing activities of rLysG1 required the integrity of the conserved α3 and 4 helixes of the protein. Together, these results provide the first insight into the activity and working mechanism of g-type lysozyme in crustacean and deep-sea organisms.     

Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. VI*

The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 389–400, 2001     

The Functional Delta Existence Theorem and the Reduction of a Proof of the Fukui Conjecture to That of the Special Functional Asymptotic Linearity Theorem

This article establishes a fundamental existence theorem, called the Functional Delta Existence Theorem (DET), which is significant for a new development in the repeat space theory (RST) and also for elucidating an empirical asymptotic principle from experimental chemistry. By using the Functional DET, we reduce a proof of the Fukui conjecture to that of a special and simpler version of the Asymptotic Linearity Theorem (ALT). This reduction provides a basis for the forthcoming series of articles entitled “Proof of the Fukui conjecture via resolution of singularities and related methods”. A proof of the Functional DET is given here in a unifying manner so that an investigative link is formed among: (i) fundamental methodology in the RST, which is referred to as the approach via the aspect of form and general topology, (ii) frontier electron theory of reactivity indices, and (iii) the Shingu–Fujimoto empirical asymptotic principle for long chain molecules.     

Chromatography: The separation technique of the 20th century

Summary M. S. Tswett contemplated the possibility of “chromatography” in 1899–1901 while carrying out his first research work on the physico-chemical structure of plant chlorophylls, and he reported “on a new category of adsorption analysis” in 1903. The evolution of chromatography followed the advances of this century: each decade brought new innovations based logically from the previous one. By the end of the 20th Century chromatography has became the most widely used separation technique in chemistry and biochemistry: thus, it is no exaggeration to call it the separation technique of the 20th Century. This paper investigates the evolution of the various branches of chromatography. An essential condition for all fruitful research is to have at one’s disposal a satisfactory technique. “Tout progrès scientific est un progrès de méthode” as somebody once remarked. Unfortunately the methodology is frequently the weakest aspect of scientific investigations.     

HOA (Heaviside Operational Ansatz) revisited: recent remarks on novel exact solution methodologies in wavefunction analysis

A viable methodology for the exact analytical solution of the multiparticle Schrodinger and Dirac equations has long been considered a holy grail of theoretical chemistry. Since a benchmark work by Torres-Vega and Frederick in the 1990s, the QPSR (Quantum Phase Space Representation) has been explored as an alternate method for solving various physical systems. Recently, the present author has developed an exact analytical symbolic solution scheme for broad classes of differential equations utilizing the HOA (Heaviside Operational Ansatz). An application of the scheme to chemical systems was initially presented in Journal of Mathematical Chemistry (Toward chemical applications of Heaviside Operational Ansatz: exact solution of radial Schrodinger equation for nonrelativistic N-particle system with pairwise 1/r(I) radial potential in quantum phase space. Journal of Mathematical Chemistry, 2009; 45(1):129–140). It is believed that the coupling of HOA with QPSR represents not only a fundamental breakthrough in theoretical physical chemistry, but it is promising as a basis for exact solution algorithms that would have tremendous impact on the capabilities of computational chemistry/physics. The novel methods allow the exact determination of the momentum [and configuration] space wavefunction from the QPSR wavefunction by way of a Fourier transform. In this note some remarks, examples and further directions, concerning HOA as a tool to solve and provide analytical insight into solutions of dynamical systems occurring in, but not limited to Mathematical Chemistry, are also posited.     

Proof of the Fukui conjecture via resolution of singularities and related methods. IV

The present article is a direct continuation of the previous part III of this series of articles, which have been devoted to cultivating a new interdisciplinary region between chemistry and mathematics. In the present part IV, we develop two sets of fundamental theoretical tools, using methods from the field of resolution of singularities and analytic curves. These two sets of tools are essential in structurally elucidating the assertion of the Fukui conjecture (concerning the additivity problems) and the crux of the functional asymptotic linearity theorem (functional ALT) that proves the conjecture in a broad context. This conjecture is a vital guideline for a future development of the repeat theory (RST)—the central unifying theory in the First and the Second Generation Fukui Project.     

Adaptive Supramolecular Networks: Emergent Sensing from Complex Systems

Molecular differentiation by supramolecular sensors is typically achieved through sensor arrays, relying on the pattern recognition responses of large panels of isolated sensing elements. Here we report a new one-pot systems chemistry approach to differential sensing in biological solutions. We constructed an adaptive network of three cross-assembling sensor elements with diverse analyte-binding and photophysical properties. This robust sensing approach exploits complex interconnected sensor-sensor and sensor-analyte equilibria, producing emergent supramolecular and photophysical responses unique to each analyte. We characterize the basic mechanisms by which an adaptive network responds to analytes. The inherently data-rich responses of an adaptive network discriminate among very closely related proteins and protein mixtures without relying on designed protein recognition elements. We show that a single adaptive sensing solution provides better analyte discrimination using fewer response observations than a sensor array built from the same components. We also show the network's ability to adapt and respond to changing biological solutions over time.     

Fabrication of microfluidic mixers and artificial vasculatures using a high-brightness diode-pumped Nd:YAG laser direct write method

This paper describes a direct write laser technology, which is fast and flexible, for fabricating multiple-level microfluidic channels. A high brightness diode-pumped Nd-YAG laser with slab geometry was used for its excellent beam quality. Channels with flat walls and staggered herringbone ridges on the floor have been successfully fabricated and their ability to perform passive mixing of liquid is discussed. Also, a multi-width multi-depth microchannel has been fabricated to generate biomimetic vasculatures whose channel diameters change according to Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughters. The multi-depth architecture allows for flow patterns to resemble physiological vascular systems with lower overall resistance and more uniform flow velocities throughout the network compared to planar patterning techniques which generate uniformly thin channels. The ability to directly fabricate multiple level structures using relatively straightforward laser technology enhances our ability to rapidly prototype complex lab-on-a-chip systems and to develop physiological microfluidic structures for tissue engineering and investigations in biomedical fluidics problems.     

The ABC of Insulin: The Organic Chemistry of a Small Protein

Insulin is a small protein crucial for regulating the blood glucose level in all animals. Since 1922 it has been used for the treatment of patients with diabetes. Despite consisting of just 51 amino acids, insulin contains 17 of the proteinogenic amino acids, A- and B-chains, three disulfide bridges, and it folds with 3 α-helices and a short β-sheet segment. Insulin associates into dimers and further into hexamers with stabilization by Zn²⁺ and phenolic ligands. Selective chemical modification of proteins is at the forefront of developments in chemical biology and biopharmaceuticals. Insulin's structure has made it amenable to organic and inorganic chemical reactions. This Review provides a synthetic organic chemistry perspective on this small protein. It gives an overview of key chemical and physico-chemical aspects of the insulin molecule, with a focus on chemoselective reactions. This includes N-acylations at the N-termini or at Lys^B29 by pH control, introduction of protecting groups on insulin, binding of metal ions, ligands to control the nano-scale assembly of insulin, and more.     

基于旋转曲面变换PSO算法的神经网络用于胺类有机物毒性分类

神经网络模型能有效地模拟非线性的输入输出关系。本研究应用三层前馈网络对51种胺类有机物进行了结构-毒性关系的分类研究。常规的神经网络权值训练算法,例如误差反传算法,存在着收敛速度慢,容易陷入局部极值点等问题。因此提出旋转曲面变换粒子群优化算法,将被优化函数的局部极小点变换为全局最大点,同时不改变比局部极小点的值更小的区域的函数形状。此方法和粒子群优化相结合,能使待优化函数跳出局部极值点,提高训练神经网络权值的效率。实验结果显示,基于旋转曲面变换粒子群优化算法的神经网络,权值训练过程收敛速度较快,且自检误差和预报误差都较小,是一种有效的胺类有机物毒性分类方法。     

The chemistry and physics of zinc oxide surfaces

Metal oxides are virtually everywhere – only gold has the property not to form an oxide on its surface when exposed to the ambient. As a result, understanding the physics and chemistry of oxide surfaces is a topic of pronounced general interest and, of course, also a necessary prerequisite for many technical applications. The most important of these is certainly heterogeneous catalysis, but one has to realize that – under ambient conditions – virtually all phenomena occurring at liquid/metal and gas/metal interfaces are determined by the corresponding oxide. This applies in particular to friction phenomena, adhesion and corrosion. A necessary – but not necessarily sufficient – condition for unravelling the fundamentals governing this complex field is to analyze in some detail elementary chemical and physical processes at oxide surfaces. Although the Surface Science of metal surfaces has seen a major progress in the past decades, for oxides detailed experimental investigations for well-defined single crystal surfaces still represent a formidable challenge – mostly because of technical difficulties (charging), but to some extent also due to fundamental problems related to the stabilization of polar surfaces. As a result, the amount of information available for this class of materials is – compared to that at hand for metals – clearly not satisfactory. A particular disturbing lack of information is that about the presence of hydrogen at oxide surfaces – either as hydroxy-species or in form of metal hydrides.In the present review we will summarize recent experimental and theoretical information which has become available from single crystal studies on ZnO surfaces. While the number of papers dealing with another oxide, rutile TiO₂, is significantly larger (although titania does not exhibit a polar surface), also for zinc oxide a basis of experimental and theoretical knowledge as been accumulated, which – at least for the non-polar surfaces – allows to understand physico-chemical processes on an atomic level for an increasing number of cases. In particular with regards to the interaction with hydrogen a number of – often surprising – observations have been reported recently. Some of them carry implications for the behaviour of hydrogen on oxide surfaces in general. We will present the currently available information for both, experiment and theory, and demonstrate the rather large variety of this material’s surface properties.     

Fundamentals and applications of near infrared spectroscopy in spectroelectrochemistry

Near infrared spectroscopy as a tool for in situ spectroelectrochemical investigations of electrochemical systems is reviewed with particular attention to experimental approaches and typical results from all parts of chemistry and applied chemistry     

计算化学辅助无机化学课堂教学模式的探索

According to the characteristics of inorganic chemistry and in view of the current problems in classroom teaching of inorganic chemistry, the computational chemistry assisted teaching model has been introduced in this paper. The implementation of this innovative model is not only helpful for students to understand the difficult knowledge of inorganic chemistry, but also popularize the practical application of computational chemistry, which provides an opportunity for the establishment of the big data platform of chemistry in colleges and universities.